Numerical Quantum Computing

Quantum Research Center, QTomo

Kyungtaek Jun: ktfriends@gmail.com
Hyunju Lee: hyunjulee0824@gmail.com

Effective QUBO formulations

Solving linear system: Ax = b
We make several QUBO models for matrices and compare the results.
From the results, we propose a new method for constrained problems.

Eigenvalues and Eigenvectors

Solving eigenvalue and eigenvector problem: Ax = kx
To solve Ax = kx, we use the two norm square of Ax - kx.
If any k and x satisfies Ax = kx, then the absolute value Ax - kx satisfies the minimum value 0.
Paper: https://www.sciencedirect.com/science/article/pii/S2666720723000243?via%3Dihub

Linear System

Solving linear system: Ax = b
To solve Ax = b, we use the two norm square of Ax - b.
If any x satisfies Ax = b, then the absolute value of Ax - b satisfies the minimum value 0.
Related preprint (with Eigenvalue problem): https://arxiv.org/abs/2106.10819

Prime factorization

Solving RSA cryptosystem: N = pq
To solve N = pq, we use the norm square of N - qp.
If p and q satisfies N = pq, then the absolute value of N - pq satisfies the minimum value 0.
Paper: https://www.nature.com/articles/s41598-023-36813-x

QAOA - Quantum Approximate Optimization Algorithm

It is an algorithm that finds the maximum value of the energy Hemiltonian used in quantum annealers in the gate model quantum computer.
We generally do QUBO modeling to use q^2 = q when creating an energy Hemiltonian.

Range dependent Hamiltonian Algorithm

We introduce an algorithm that can be used by dividing the size of the entire domain according to the number of qubits.
We also form a QUBO model related to each subregion. 
Related preprint: https://arxiv.org/abs/2202.07692